| 1 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "xhtml1-transitional.dtd"> |
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| 3 | <?xml-stylesheet type="text/xsl" href="mathml.xsl"?><html xmlns="http://www.w3.org/1999/xhtml" xmlns:pref="http://www.w3.org/2002/Math/preference" pref:renderer="mathplayer-dl"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>glMap2</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2" /></head><body><div class="refentry" lang="en" xml:lang="en"><a id="glMap2"></a><div class="titlepage"></div><div class="refnamediv"><h2>Name</h2><p>glMap2 — define a two-dimensional evaluator</p></div><div class="refsynopsisdiv"><h2>C Specification</h2><div class="funcsynopsis"><table border="0" summary="Function synopsis" cellspacing="0" cellpadding="0"><tr><td><code class="funcdef">void <b class="fsfunc">glMap2f</b>(</code></td><td>GLenum </td><td><var class="pdparam">target</var>, </td></tr><tr><td> </td><td>GLfloat </td><td><var class="pdparam">u1</var>, </td></tr><tr><td> </td><td>GLfloat </td><td><var class="pdparam">u2</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">ustride</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">uorder</var>, </td></tr><tr><td> </td><td>GLfloat </td><td><var class="pdparam">v1</var>, </td></tr><tr><td> </td><td>GLfloat </td><td><var class="pdparam">v2</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">vstride</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">vorder</var>, </td></tr><tr><td> </td><td>const GLfloat * </td><td><var class="pdparam">points</var><code>)</code>;</td></tr></table></div><div class="funcsynopsis"><table border="0" summary="Function synopsis" cellspacing="0" cellpadding="0"><tr><td><code class="funcdef">void <b class="fsfunc">glMap2d</b>(</code></td><td>GLenum </td><td><var class="pdparam">target</var>, </td></tr><tr><td> </td><td>GLdouble </td><td><var class="pdparam">u1</var>, </td></tr><tr><td> </td><td>GLdouble </td><td><var class="pdparam">u2</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">ustride</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">uorder</var>, </td></tr><tr><td> </td><td>GLdouble </td><td><var class="pdparam">v1</var>, </td></tr><tr><td> </td><td>GLdouble </td><td><var class="pdparam">v2</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">vstride</var>, </td></tr><tr><td> </td><td>GLint </td><td><var class="pdparam">vorder</var>, </td></tr><tr><td> </td><td>const GLdouble * </td><td><var class="pdparam">points</var><code>)</code>;</td></tr></table></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="parameters"></a><h2>Parameters</h2><div class="variablelist"><dl><dt><span class="term"><em class="parameter"><code>target</code></em></span></dt><dd><p> |
| 4 | Specifies the kind of values that are generated by the evaluator. |
| 5 | Symbolic constants |
| 6 | <code class="constant">GL_MAP2_VERTEX_3</code>, |
| 7 | <code class="constant">GL_MAP2_VERTEX_4</code>, |
| 8 | <code class="constant">GL_MAP2_INDEX</code>, |
| 9 | <code class="constant">GL_MAP2_COLOR_4</code>, |
| 10 | <code class="constant">GL_MAP2_NORMAL</code>, |
| 11 | <code class="constant">GL_MAP2_TEXTURE_COORD_1</code>, |
| 12 | <code class="constant">GL_MAP2_TEXTURE_COORD_2</code>, |
| 13 | <code class="constant">GL_MAP2_TEXTURE_COORD_3</code>, and |
| 14 | <code class="constant">GL_MAP2_TEXTURE_COORD_4</code> are accepted. |
| 15 | </p></dd><dt><span class="term"><em class="parameter"><code>u1</code></em>, </span><span class="term"><em class="parameter"><code>u2</code></em></span></dt><dd><p> |
| 16 | Specify a linear mapping of |
| 17 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">u</mml:mi></mml:math>, |
| 18 | as presented to <a class="citerefentry" href="glEvalCoord2.xml"><span class="citerefentry"><span class="refentrytitle">glEvalCoord2</span></span></a>, |
| 19 | to |
| 20 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 21 | |
| 22 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 23 | </mml:math>, |
| 24 | one of the two variables that are evaluated by the equations specified |
| 25 | by this command. Initially, <em class="parameter"><code>u1</code></em> is 0 and <em class="parameter"><code>u2</code></em> is 1. |
| 26 | </p></dd><dt><span class="term"><em class="parameter"><code>ustride</code></em></span></dt><dd><p> |
| 27 | Specifies the number of floats or doubles between |
| 28 | the beginning of control point |
| 29 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 30 | |
| 31 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 32 | <mml:mi mathvariant="italic">ij</mml:mi> |
| 33 | </mml:msub> |
| 34 | </mml:math> |
| 35 | and the beginning of control point |
| 36 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 37 | |
| 38 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 39 | <mml:mfenced open="" close=""> |
| 40 | <mml:mrow> |
| 41 | <mml:mfenced open="(" close=")"> |
| 42 | <mml:mrow> |
| 43 | <mml:mi mathvariant="italic">i</mml:mi> |
| 44 | <mml:mo>+</mml:mo> |
| 45 | <mml:mn>1</mml:mn> |
| 46 | </mml:mrow> |
| 47 | </mml:mfenced> |
| 48 | <mml:mo></mml:mo> |
| 49 | <mml:mi mathvariant="italic">j</mml:mi> |
| 50 | </mml:mrow> |
| 51 | </mml:mfenced> |
| 52 | </mml:msub> |
| 53 | </mml:math>, |
| 54 | where |
| 55 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">i</mml:mi></mml:math> |
| 56 | and |
| 57 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">j</mml:mi></mml:math> |
| 58 | are the |
| 59 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">u</mml:mi></mml:math> |
| 60 | and |
| 61 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">v</mml:mi></mml:math> |
| 62 | control point indices, respectively. |
| 63 | This allows control points to be embedded in arbitrary data structures. |
| 64 | The only constraint is that the values for a particular control point |
| 65 | must occupy contiguous memory locations. The initial value of <em class="parameter"><code>ustride</code></em> is 0. |
| 66 | </p></dd><dt><span class="term"><em class="parameter"><code>uorder</code></em></span></dt><dd><p> |
| 67 | Specifies the dimension of the control point array in the |
| 68 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">u</mml:mi></mml:math> |
| 69 | axis. |
| 70 | Must be positive. The initial value is 1. |
| 71 | </p></dd><dt><span class="term"><em class="parameter"><code>v1</code></em>, </span><span class="term"><em class="parameter"><code>v2</code></em></span></dt><dd><p> |
| 72 | Specify a linear mapping of |
| 73 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">v</mml:mi></mml:math>, |
| 74 | as presented to <a class="citerefentry" href="glEvalCoord2.xml"><span class="citerefentry"><span class="refentrytitle">glEvalCoord2</span></span></a>, |
| 75 | to |
| 76 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 77 | |
| 78 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 79 | </mml:math>, |
| 80 | one of the two variables that are evaluated by the equations specified |
| 81 | by this command. Initially, <em class="parameter"><code>v1</code></em> is 0 and <em class="parameter"><code>v2</code></em> is 1. |
| 82 | </p></dd><dt><span class="term"><em class="parameter"><code>vstride</code></em></span></dt><dd><p> |
| 83 | Specifies the number of floats or doubles between |
| 84 | the beginning of control point |
| 85 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 86 | |
| 87 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 88 | <mml:mi mathvariant="italic">ij</mml:mi> |
| 89 | </mml:msub> |
| 90 | </mml:math> |
| 91 | and the beginning of control point |
| 92 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 93 | |
| 94 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 95 | <mml:mfenced open="" close=""> |
| 96 | <mml:mrow> |
| 97 | <mml:mi mathvariant="italic">i</mml:mi> |
| 98 | <mml:mo></mml:mo> |
| 99 | <mml:mfenced open="(" close=")"> |
| 100 | <mml:mrow> |
| 101 | <mml:mi mathvariant="italic">j</mml:mi> |
| 102 | <mml:mo>+</mml:mo> |
| 103 | <mml:mn>1</mml:mn> |
| 104 | </mml:mrow> |
| 105 | </mml:mfenced> |
| 106 | </mml:mrow> |
| 107 | </mml:mfenced> |
| 108 | </mml:msub> |
| 109 | </mml:math>, |
| 110 | where |
| 111 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">i</mml:mi></mml:math> |
| 112 | and |
| 113 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">j</mml:mi></mml:math> |
| 114 | are the |
| 115 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">u</mml:mi></mml:math> |
| 116 | and |
| 117 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">v</mml:mi></mml:math> |
| 118 | control point indices, respectively. |
| 119 | This allows control points to be embedded in arbitrary data structures. |
| 120 | The only constraint is that the values for a particular control point |
| 121 | must occupy contiguous memory locations. The initial value of <em class="parameter"><code>vstride</code></em> is 0. |
| 122 | </p></dd><dt><span class="term"><em class="parameter"><code>vorder</code></em></span></dt><dd><p> |
| 123 | Specifies the dimension of the control point array in the |
| 124 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">v</mml:mi></mml:math> |
| 125 | axis. |
| 126 | Must be positive. The initial value is 1. |
| 127 | </p></dd><dt><span class="term"><em class="parameter"><code>points</code></em></span></dt><dd><p> |
| 128 | Specifies a pointer to the array of control points. |
| 129 | </p></dd></dl></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="description"></a><h2>Description</h2><p> |
| 130 | Evaluators provide a way to use polynomial or rational polynomial mapping |
| 131 | to produce vertices, |
| 132 | normals, |
| 133 | texture coordinates, |
| 134 | and colors. |
| 135 | The values produced by an evaluator are sent on to further stages |
| 136 | of GL processing just as if they had been presented using |
| 137 | <a class="citerefentry" href="glVertex.xml"><span class="citerefentry"><span class="refentrytitle">glVertex</span></span></a>, |
| 138 | <a class="citerefentry" href="glNormal.xml"><span class="citerefentry"><span class="refentrytitle">glNormal</span></span></a>, |
| 139 | <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a>, and |
| 140 | <a class="citerefentry" href="glColor.xml"><span class="citerefentry"><span class="refentrytitle">glColor</span></span></a> commands, |
| 141 | except that the generated values do not update the current normal, |
| 142 | texture coordinates, |
| 143 | or color. |
| 144 | </p><p> |
| 145 | All polynomial or rational polynomial splines of any degree |
| 146 | (up to the maximum degree supported by the GL implementation) |
| 147 | can be described using evaluators. |
| 148 | These include almost all surfaces used in computer graphics, |
| 149 | including B-spline surfaces, |
| 150 | NURBS surfaces, |
| 151 | Bezier surfaces, and so on. |
| 152 | </p><p> |
| 153 | Evaluators define surfaces based on bivariate Bernstein polynomials. |
| 154 | Define |
| 155 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 156 | |
| 157 | <mml:mrow> |
| 158 | <mml:mi mathvariant="italic">p</mml:mi> |
| 159 | <mml:mo></mml:mo> |
| 160 | <mml:mfenced open="(" close=")"> |
| 161 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 162 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 163 | </mml:mfenced> |
| 164 | </mml:mrow> |
| 165 | </mml:math> |
| 166 | as |
| 167 | </p><p> |
| 168 | </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 169 | |
| 170 | <mml:mrow> |
| 171 | <mml:mrow> |
| 172 | <mml:mi mathvariant="italic">p</mml:mi> |
| 173 | <mml:mo></mml:mo> |
| 174 | <mml:mfenced open="(" close=")"> |
| 175 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 176 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 177 | </mml:mfenced> |
| 178 | </mml:mrow> |
| 179 | <mml:mo>=</mml:mo> |
| 180 | <mml:mrow> |
| 181 | <mml:munderover> |
| 182 | <mml:mo>Σ</mml:mo> |
| 183 | <mml:mrow> |
| 184 | <mml:mi mathvariant="italic">i</mml:mi> |
| 185 | <mml:mo>=</mml:mo> |
| 186 | <mml:mn>0</mml:mn> |
| 187 | </mml:mrow> |
| 188 | <mml:mi mathvariant="italic">n</mml:mi> |
| 189 | </mml:munderover> |
| 190 | <mml:mrow> |
| 191 | <mml:munderover> |
| 192 | <mml:mo>Σ</mml:mo> |
| 193 | <mml:mrow> |
| 194 | <mml:mi mathvariant="italic">j</mml:mi> |
| 195 | <mml:mo>=</mml:mo> |
| 196 | <mml:mn>0</mml:mn> |
| 197 | </mml:mrow> |
| 198 | <mml:mi mathvariant="italic">m</mml:mi> |
| 199 | </mml:munderover> |
| 200 | <mml:mrow> |
| 201 | <mml:mrow> |
| 202 | <mml:msup><mml:mfenced open="" close=""> |
| 203 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 204 | <mml:mi mathvariant="italic">i</mml:mi> |
| 205 | </mml:msub> |
| 206 | </mml:mfenced> |
| 207 | <mml:mi mathvariant="italic">n</mml:mi> |
| 208 | </mml:msup> |
| 209 | <mml:mo></mml:mo> |
| 210 | <mml:mfenced open="(" close=")"> |
| 211 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 212 | </mml:mfenced> |
| 213 | </mml:mrow> |
| 214 | <mml:mo></mml:mo> |
| 215 | <mml:mrow> |
| 216 | <mml:msup><mml:mfenced open="" close=""> |
| 217 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 218 | <mml:mi mathvariant="italic">j</mml:mi> |
| 219 | </mml:msub> |
| 220 | </mml:mfenced> |
| 221 | <mml:mi mathvariant="italic">m</mml:mi> |
| 222 | </mml:msup> |
| 223 | <mml:mo></mml:mo> |
| 224 | <mml:mfenced open="(" close=")"> |
| 225 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 226 | </mml:mfenced> |
| 227 | </mml:mrow> |
| 228 | <mml:mo></mml:mo> |
| 229 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 230 | <mml:mi mathvariant="italic">ij</mml:mi> |
| 231 | </mml:msub> |
| 232 | </mml:mrow> |
| 233 | </mml:mrow> |
| 234 | </mml:mrow> |
| 235 | </mml:mrow> |
| 236 | </mml:math></div><p> |
| 237 | </p><p> |
| 238 | </p><p> |
| 239 | where |
| 240 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 241 | |
| 242 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 243 | <mml:mi mathvariant="italic">ij</mml:mi> |
| 244 | </mml:msub> |
| 245 | </mml:math> |
| 246 | is a control point, |
| 247 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 248 | |
| 249 | <mml:mrow> |
| 250 | <mml:msup><mml:mfenced open="" close=""> |
| 251 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 252 | <mml:mi mathvariant="italic">i</mml:mi> |
| 253 | </mml:msub> |
| 254 | </mml:mfenced> |
| 255 | <mml:mi mathvariant="italic">n</mml:mi> |
| 256 | </mml:msup> |
| 257 | <mml:mo></mml:mo> |
| 258 | <mml:mfenced open="(" close=")"> |
| 259 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 260 | </mml:mfenced> |
| 261 | </mml:mrow> |
| 262 | </mml:math> |
| 263 | is the |
| 264 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">i</mml:mi></mml:math>th |
| 265 | Bernstein polynomial of degree |
| 266 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">n</mml:mi></mml:math> |
| 267 | (<em class="parameter"><code>uorder</code></em> = |
| 268 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 269 | |
| 270 | <mml:mrow> |
| 271 | <mml:mi mathvariant="italic">n</mml:mi> |
| 272 | <mml:mo>+</mml:mo> |
| 273 | <mml:mn>1</mml:mn> |
| 274 | </mml:mrow> |
| 275 | </mml:math>) |
| 276 | </p><p> |
| 277 | </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 278 | |
| 279 | <mml:mrow> |
| 280 | <mml:mrow> |
| 281 | <mml:msup><mml:mfenced open="" close=""> |
| 282 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 283 | <mml:mi mathvariant="italic">i</mml:mi> |
| 284 | </mml:msub> |
| 285 | </mml:mfenced> |
| 286 | <mml:mi mathvariant="italic">n</mml:mi> |
| 287 | </mml:msup> |
| 288 | <mml:mo></mml:mo> |
| 289 | <mml:mfenced open="(" close=")"> |
| 290 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 291 | </mml:mfenced> |
| 292 | </mml:mrow> |
| 293 | <mml:mo>=</mml:mo> |
| 294 | <mml:mrow> |
| 295 | <mml:mfenced open="(" close=")"> |
| 296 | <mml:mfenced open="" close=""> |
| 297 | <mml:mtable> |
| 298 | <mml:mtr><mml:mtd> |
| 299 | <mml:mi mathvariant="italic">n</mml:mi> |
| 300 | </mml:mtd></mml:mtr> |
| 301 | <mml:mtr><mml:mtd> |
| 302 | <mml:mi mathvariant="italic">i</mml:mi> |
| 303 | </mml:mtd></mml:mtr> |
| 304 | </mml:mtable> |
| 305 | </mml:mfenced> |
| 306 | </mml:mfenced> |
| 307 | <mml:mo></mml:mo> |
| 308 | <mml:msup><mml:mfenced open="" close=""> |
| 309 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 310 | </mml:mfenced> |
| 311 | <mml:mi mathvariant="italic">i</mml:mi> |
| 312 | </mml:msup> |
| 313 | <mml:mo></mml:mo> |
| 314 | <mml:mfenced open="" close=""> |
| 315 | <mml:msup><mml:mfenced open="(" close=")"> |
| 316 | <mml:mrow> |
| 317 | <mml:mn>1</mml:mn> |
| 318 | <mml:mo>-</mml:mo> |
| 319 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 320 | </mml:mrow> |
| 321 | </mml:mfenced> |
| 322 | <mml:mfenced open="" close=""> |
| 323 | <mml:mrow> |
| 324 | <mml:mi mathvariant="italic">n</mml:mi> |
| 325 | <mml:mo>-</mml:mo> |
| 326 | <mml:mi mathvariant="italic">i</mml:mi> |
| 327 | </mml:mrow> |
| 328 | </mml:mfenced> |
| 329 | </mml:msup> |
| 330 | </mml:mfenced> |
| 331 | </mml:mrow> |
| 332 | </mml:mrow> |
| 333 | </mml:math></div><p> |
| 334 | </p><p> |
| 335 | and |
| 336 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 337 | |
| 338 | <mml:mrow> |
| 339 | <mml:msup><mml:mfenced open="" close=""> |
| 340 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 341 | <mml:mi mathvariant="italic">j</mml:mi> |
| 342 | </mml:msub> |
| 343 | </mml:mfenced> |
| 344 | <mml:mi mathvariant="italic">m</mml:mi> |
| 345 | </mml:msup> |
| 346 | <mml:mo></mml:mo> |
| 347 | <mml:mfenced open="(" close=")"> |
| 348 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 349 | </mml:mfenced> |
| 350 | </mml:mrow> |
| 351 | </mml:math> |
| 352 | is the |
| 353 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">j</mml:mi></mml:math>th |
| 354 | Bernstein polynomial of degree |
| 355 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">m</mml:mi></mml:math> |
| 356 | (<em class="parameter"><code>vorder</code></em> = |
| 357 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 358 | |
| 359 | <mml:mrow> |
| 360 | <mml:mi mathvariant="italic">m</mml:mi> |
| 361 | <mml:mo>+</mml:mo> |
| 362 | <mml:mn>1</mml:mn> |
| 363 | </mml:mrow> |
| 364 | </mml:math>) |
| 365 | </p><p> |
| 366 | </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 367 | |
| 368 | <mml:mrow> |
| 369 | <mml:mrow> |
| 370 | <mml:msup><mml:mfenced open="" close=""> |
| 371 | <mml:msub><mml:mi mathvariant="italic">B</mml:mi> |
| 372 | <mml:mi mathvariant="italic">j</mml:mi> |
| 373 | </mml:msub> |
| 374 | </mml:mfenced> |
| 375 | <mml:mi mathvariant="italic">m</mml:mi> |
| 376 | </mml:msup> |
| 377 | <mml:mo></mml:mo> |
| 378 | <mml:mfenced open="(" close=")"> |
| 379 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 380 | </mml:mfenced> |
| 381 | </mml:mrow> |
| 382 | <mml:mo>=</mml:mo> |
| 383 | <mml:mrow> |
| 384 | <mml:mfenced open="(" close=")"> |
| 385 | <mml:mfenced open="" close=""> |
| 386 | <mml:mtable> |
| 387 | <mml:mtr><mml:mtd> |
| 388 | <mml:mi mathvariant="italic">m</mml:mi> |
| 389 | </mml:mtd></mml:mtr> |
| 390 | <mml:mtr><mml:mtd> |
| 391 | <mml:mi mathvariant="italic">j</mml:mi> |
| 392 | </mml:mtd></mml:mtr> |
| 393 | </mml:mtable> |
| 394 | </mml:mfenced> |
| 395 | </mml:mfenced> |
| 396 | <mml:mo></mml:mo> |
| 397 | <mml:msup><mml:mfenced open="" close=""> |
| 398 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 399 | </mml:mfenced> |
| 400 | <mml:mi mathvariant="italic">j</mml:mi> |
| 401 | </mml:msup> |
| 402 | <mml:mo></mml:mo> |
| 403 | <mml:mfenced open="" close=""> |
| 404 | <mml:msup><mml:mfenced open="(" close=")"> |
| 405 | <mml:mrow> |
| 406 | <mml:mn>1</mml:mn> |
| 407 | <mml:mo>-</mml:mo> |
| 408 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 409 | </mml:mrow> |
| 410 | </mml:mfenced> |
| 411 | <mml:mfenced open="" close=""> |
| 412 | <mml:mrow> |
| 413 | <mml:mi mathvariant="italic">m</mml:mi> |
| 414 | <mml:mo>-</mml:mo> |
| 415 | <mml:mi mathvariant="italic">j</mml:mi> |
| 416 | </mml:mrow> |
| 417 | </mml:mfenced> |
| 418 | </mml:msup> |
| 419 | </mml:mfenced> |
| 420 | </mml:mrow> |
| 421 | </mml:mrow> |
| 422 | </mml:math></div><p> |
| 423 | </p><p> |
| 424 | Recall that |
| 425 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 426 | |
| 427 | <mml:mrow> |
| 428 | <mml:msup><mml:mn>0</mml:mn> |
| 429 | <mml:mn>0</mml:mn> |
| 430 | </mml:msup> |
| 431 | <mml:mo>==</mml:mo> |
| 432 | <mml:mn>1</mml:mn> |
| 433 | </mml:mrow> |
| 434 | </mml:math> |
| 435 | and |
| 436 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 437 | |
| 438 | <mml:mrow> |
| 439 | <mml:mfenced open="(" close=")"> |
| 440 | <mml:mfenced open="" close=""> |
| 441 | <mml:mtable> |
| 442 | <mml:mtr><mml:mtd> |
| 443 | <mml:mi mathvariant="italic">n</mml:mi> |
| 444 | </mml:mtd></mml:mtr> |
| 445 | <mml:mtr><mml:mtd> |
| 446 | <mml:mn>0</mml:mn> |
| 447 | </mml:mtd></mml:mtr> |
| 448 | </mml:mtable> |
| 449 | </mml:mfenced> |
| 450 | </mml:mfenced> |
| 451 | <mml:mo>==</mml:mo> |
| 452 | <mml:mn>1</mml:mn> |
| 453 | </mml:mrow> |
| 454 | </mml:math> |
| 455 | </p><p> |
| 456 | <code class="function">glMap2</code> is used to define the basis and to specify what kind of values |
| 457 | are produced. |
| 458 | Once defined, |
| 459 | a map can be enabled and disabled by calling <a class="citerefentry" href="glEnable.xml"><span class="citerefentry"><span class="refentrytitle">glEnable</span></span></a> and <a class="citerefentry" href="glDisable.xml"><span class="citerefentry"><span class="refentrytitle">glDisable</span></span></a> |
| 460 | with the map name, one of the nine predefined values for <em class="parameter"><code>target</code></em>, |
| 461 | described below. |
| 462 | When <a class="citerefentry" href="glEvalCoord2.xml"><span class="citerefentry"><span class="refentrytitle">glEvalCoord2</span></span></a> presents values |
| 463 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">u</mml:mi></mml:math> |
| 464 | and |
| 465 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">v</mml:mi></mml:math>, |
| 466 | the bivariate Bernstein polynomials are evaluated using |
| 467 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 468 | |
| 469 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 470 | </mml:math> |
| 471 | and |
| 472 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 473 | |
| 474 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 475 | </mml:math>, |
| 476 | where |
| 477 | </p><p> |
| 478 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 479 | |
| 480 | <mml:mrow> |
| 481 | <mml:mover><mml:mi mathvariant="italic">u</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 482 | <mml:mo>=</mml:mo> |
| 483 | <mml:mfrac> |
| 484 | <mml:mfenced open="" close=""> |
| 485 | <mml:mrow> |
| 486 | <mml:mi mathvariant="italic">u</mml:mi> |
| 487 | <mml:mo>-</mml:mo> |
| 488 | <mml:mi mathvariant="italic">u1</mml:mi> |
| 489 | </mml:mrow> |
| 490 | </mml:mfenced> |
| 491 | <mml:mfenced open="" close=""> |
| 492 | <mml:mrow> |
| 493 | <mml:mi mathvariant="italic">u2</mml:mi> |
| 494 | <mml:mo>-</mml:mo> |
| 495 | <mml:mi mathvariant="italic">u1</mml:mi> |
| 496 | </mml:mrow> |
| 497 | </mml:mfenced> |
| 498 | </mml:mfrac> |
| 499 | </mml:mrow> |
| 500 | </mml:math> |
| 501 | </p><p> |
| 502 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 503 | |
| 504 | <mml:mrow> |
| 505 | <mml:mover><mml:mi mathvariant="italic">v</mml:mi><mml:mo>̂</mml:mo></mml:mover> |
| 506 | <mml:mo>=</mml:mo> |
| 507 | <mml:mfrac> |
| 508 | <mml:mfenced open="" close=""> |
| 509 | <mml:mrow> |
| 510 | <mml:mi mathvariant="italic">v</mml:mi> |
| 511 | <mml:mo>-</mml:mo> |
| 512 | <mml:mi mathvariant="italic">v1</mml:mi> |
| 513 | </mml:mrow> |
| 514 | </mml:mfenced> |
| 515 | <mml:mfenced open="" close=""> |
| 516 | <mml:mrow> |
| 517 | <mml:mi mathvariant="italic">v2</mml:mi> |
| 518 | <mml:mo>-</mml:mo> |
| 519 | <mml:mi mathvariant="italic">v1</mml:mi> |
| 520 | </mml:mrow> |
| 521 | </mml:mfenced> |
| 522 | </mml:mfrac> |
| 523 | </mml:mrow> |
| 524 | </mml:math> |
| 525 | </p><p> |
| 526 | <em class="parameter"><code>target</code></em> is a symbolic constant that indicates what kind of control points |
| 527 | are provided in <em class="parameter"><code>points</code></em>, |
| 528 | and what output is generated when the map is evaluated. |
| 529 | It can assume one of nine predefined values: |
| 530 | </p><div class="variablelist"><dl><dt><span class="term"><code class="constant">GL_MAP2_VERTEX_3</code></span></dt><dd><p> |
| 531 | Each control point is three floating-point values representing |
| 532 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">x</mml:mi></mml:math>, |
| 533 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">y</mml:mi></mml:math>, |
| 534 | and |
| 535 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">z</mml:mi></mml:math>. |
| 536 | Internal <a class="citerefentry" href="glVertex3.xml"><span class="citerefentry"><span class="refentrytitle">glVertex3</span></span></a> commands are generated when the map is evaluated. |
| 537 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_VERTEX_4</code></span></dt><dd><p> |
| 538 | Each control point is four floating-point values representing |
| 539 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">x</mml:mi></mml:math>, |
| 540 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">y</mml:mi></mml:math>, |
| 541 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">z</mml:mi></mml:math>, |
| 542 | and |
| 543 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">w</mml:mi></mml:math>. |
| 544 | Internal <a class="citerefentry" href="glVertex4.xml"><span class="citerefentry"><span class="refentrytitle">glVertex4</span></span></a> commands are generated when the map is evaluated. |
| 545 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_INDEX</code></span></dt><dd><p> |
| 546 | Each control point is a single floating-point value representing a color index. |
| 547 | Internal <a class="citerefentry" href="glIndex.xml"><span class="citerefentry"><span class="refentrytitle">glIndex</span></span></a> commands are generated when the map is evaluated |
| 548 | but the current index is not updated with the value of these |
| 549 | <a class="citerefentry" href="glIndex.xml"><span class="citerefentry"><span class="refentrytitle">glIndex</span></span></a> commands. |
| 550 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_COLOR_4</code></span></dt><dd><p> |
| 551 | Each control point is four floating-point values representing |
| 552 | red, green, blue, and alpha. |
| 553 | Internal <a class="citerefentry" href="glColor4.xml"><span class="citerefentry"><span class="refentrytitle">glColor4</span></span></a> commands are generated when the map is |
| 554 | evaluated but the current color is not updated with the value of |
| 555 | these <a class="citerefentry" href="glColor4.xml"><span class="citerefentry"><span class="refentrytitle">glColor4</span></span></a> commands. |
| 556 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_NORMAL</code></span></dt><dd><p> |
| 557 | Each control point is three floating-point values representing |
| 558 | the |
| 559 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">x</mml:mi></mml:math>, |
| 560 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">y</mml:mi></mml:math>, |
| 561 | and |
| 562 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">z</mml:mi></mml:math> |
| 563 | components of a normal vector. |
| 564 | Internal <a class="citerefentry" href="glNormal.xml"><span class="citerefentry"><span class="refentrytitle">glNormal</span></span></a> commands are generated when the map is |
| 565 | evaluated but the current normal is not updated with the value of |
| 566 | these <a class="citerefentry" href="glNormal.xml"><span class="citerefentry"><span class="refentrytitle">glNormal</span></span></a> commands. |
| 567 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_TEXTURE_COORD_1</code></span></dt><dd><p> |
| 568 | Each control point is a single floating-point value representing |
| 569 | the |
| 570 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">s</mml:mi></mml:math> |
| 571 | texture coordinate. |
| 572 | Internal |
| 573 | <a class="citerefentry" href="glTexCoord1.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord1</span></span></a> commands are generated when the map is evaluated but |
| 574 | the current texture coordinates are not updated with the value |
| 575 | of these <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a> commands. |
| 576 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_TEXTURE_COORD_2</code></span></dt><dd><p> |
| 577 | Each control point is two floating-point values representing |
| 578 | the |
| 579 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">s</mml:mi></mml:math> |
| 580 | and |
| 581 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">t</mml:mi></mml:math> |
| 582 | texture coordinates. |
| 583 | Internal |
| 584 | <a class="citerefentry" href="glTexCoord2.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord2</span></span></a> commands are generated when the map is evaluated but |
| 585 | the current texture coordinates are not updated with the value |
| 586 | of these <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a> commands. |
| 587 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_TEXTURE_COORD_3</code></span></dt><dd><p> |
| 588 | Each control point is three floating-point values representing |
| 589 | the |
| 590 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">s</mml:mi></mml:math>, |
| 591 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">t</mml:mi></mml:math>, |
| 592 | and |
| 593 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">r</mml:mi></mml:math> |
| 594 | texture coordinates. |
| 595 | Internal <a class="citerefentry" href="glTexCoord3.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord3</span></span></a> commands are generated when the map is |
| 596 | evaluated but the current texture coordinates are not updated with the value |
| 597 | of these <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a> commands. |
| 598 | </p></dd><dt><span class="term"><code class="constant">GL_MAP2_TEXTURE_COORD_4</code></span></dt><dd><p> |
| 599 | Each control point is four floating-point values representing |
| 600 | the |
| 601 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">s</mml:mi></mml:math>, |
| 602 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">t</mml:mi></mml:math>, |
| 603 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">r</mml:mi></mml:math>, |
| 604 | and |
| 605 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">q</mml:mi></mml:math> |
| 606 | texture coordinates. |
| 607 | Internal |
| 608 | <a class="citerefentry" href="glTexCoord4.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord4</span></span></a> commands are generated when the map is evaluated but the current texture coordinates are not updated with the value |
| 609 | of these <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a> commands. |
| 610 | </p></dd></dl></div><p> |
| 611 | <em class="parameter"><code>ustride</code></em>, |
| 612 | <em class="parameter"><code>uorder</code></em>, |
| 613 | <em class="parameter"><code>vstride</code></em>, |
| 614 | <em class="parameter"><code>vorder</code></em>, and |
| 615 | <em class="parameter"><code>points</code></em> define the array addressing for accessing the control points. |
| 616 | <em class="parameter"><code>points</code></em> is the location of the first control point, |
| 617 | which occupies one, two, three, or four contiguous memory locations, |
| 618 | depending on which map is being defined. |
| 619 | There are |
| 620 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 621 | |
| 622 | <mml:mrow> |
| 623 | <mml:mi mathvariant="italic">uorder</mml:mi> |
| 624 | <mml:mo>×</mml:mo> |
| 625 | <mml:mi mathvariant="italic">vorder</mml:mi> |
| 626 | </mml:mrow> |
| 627 | </mml:math> |
| 628 | control points in the array. |
| 629 | <em class="parameter"><code>ustride</code></em> specifies how many float or double locations are skipped to advance |
| 630 | the internal memory pointer from control point |
| 631 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 632 | |
| 633 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 634 | <mml:mfenced open="" close=""> |
| 635 | <mml:mrow> |
| 636 | <mml:mi mathvariant="italic">i</mml:mi> |
| 637 | <mml:mo></mml:mo> |
| 638 | <mml:mi mathvariant="italic">j</mml:mi> |
| 639 | </mml:mrow> |
| 640 | </mml:mfenced> |
| 641 | </mml:msub> |
| 642 | </mml:math> |
| 643 | to control point |
| 644 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 645 | |
| 646 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 647 | <mml:mfenced open="" close=""> |
| 648 | <mml:mrow> |
| 649 | <mml:mfenced open="(" close=")"> |
| 650 | <mml:mrow> |
| 651 | <mml:mi mathvariant="italic">i</mml:mi> |
| 652 | <mml:mo>+</mml:mo> |
| 653 | <mml:mn>1</mml:mn> |
| 654 | </mml:mrow> |
| 655 | </mml:mfenced> |
| 656 | <mml:mo></mml:mo> |
| 657 | <mml:mi mathvariant="italic">j</mml:mi> |
| 658 | </mml:mrow> |
| 659 | </mml:mfenced> |
| 660 | </mml:msub> |
| 661 | </mml:math>. |
| 662 | <em class="parameter"><code>vstride</code></em> specifies how many float or double locations are skipped to advance |
| 663 | the internal memory pointer from control point |
| 664 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 665 | |
| 666 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 667 | <mml:mfenced open="" close=""> |
| 668 | <mml:mrow> |
| 669 | <mml:mi mathvariant="italic">i</mml:mi> |
| 670 | <mml:mo></mml:mo> |
| 671 | <mml:mi mathvariant="italic">j</mml:mi> |
| 672 | </mml:mrow> |
| 673 | </mml:mfenced> |
| 674 | </mml:msub> |
| 675 | </mml:math> |
| 676 | to control point |
| 677 | <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> |
| 678 | |
| 679 | <mml:msub><mml:mi mathvariant="italic">R</mml:mi> |
| 680 | <mml:mfenced open="" close=""> |
| 681 | <mml:mrow> |
| 682 | <mml:mi mathvariant="italic">i</mml:mi> |
| 683 | <mml:mo></mml:mo> |
| 684 | <mml:mfenced open="(" close=")"> |
| 685 | <mml:mrow> |
| 686 | <mml:mi mathvariant="italic">j</mml:mi> |
| 687 | <mml:mo>+</mml:mo> |
| 688 | <mml:mn>1</mml:mn> |
| 689 | </mml:mrow> |
| 690 | </mml:mfenced> |
| 691 | </mml:mrow> |
| 692 | </mml:mfenced> |
| 693 | </mml:msub> |
| 694 | </mml:math>. |
| 695 | </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="notes"></a><h2>Notes</h2><p> |
| 696 | As is the case with all GL commands that accept pointers to data, |
| 697 | it is as if the contents of <em class="parameter"><code>points</code></em> were copied by <code class="function">glMap2</code> before <code class="function">glMap2</code> |
| 698 | returns. |
| 699 | Changes to the contents of <em class="parameter"><code>points</code></em> have no effect after <code class="function">glMap2</code> is called. |
| 700 | </p><p> |
| 701 | Initially, <code class="constant">GL_AUTO_NORMAL</code> is enabled. If <code class="constant">GL_AUTO_NORMAL</code> is enabled, |
| 702 | normal vectors are generated when either |
| 703 | <code class="constant">GL_MAP2_VERTEX_3</code> or <code class="constant">GL_MAP2_VERTEX_4</code> is used to generate |
| 704 | vertices. |
| 705 | </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="errors"></a><h2>Errors</h2><p> |
| 706 | <code class="constant">GL_INVALID_ENUM</code> is generated if <em class="parameter"><code>target</code></em> is not an accepted value. |
| 707 | </p><p> |
| 708 | <code class="constant">GL_INVALID_VALUE</code> is generated if <em class="parameter"><code>u1</code></em> is equal to <em class="parameter"><code>u2</code></em>, |
| 709 | or if <em class="parameter"><code>v1</code></em> is equal to <em class="parameter"><code>v2</code></em>. |
| 710 | </p><p> |
| 711 | <code class="constant">GL_INVALID_VALUE</code> is generated if either <em class="parameter"><code>ustride</code></em> or <em class="parameter"><code>vstride</code></em> |
| 712 | is less than the number of values in a control point. |
| 713 | </p><p> |
| 714 | <code class="constant">GL_INVALID_VALUE</code> is generated if either <em class="parameter"><code>uorder</code></em> or <em class="parameter"><code>vorder</code></em> |
| 715 | is less than 1 or greater than the return value of <code class="constant">GL_MAX_EVAL_ORDER</code>. |
| 716 | </p><p> |
| 717 | <code class="constant">GL_INVALID_OPERATION</code> is generated if <code class="function">glMap2</code> |
| 718 | is executed between the execution of |
| 719 | <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a> |
| 720 | and the corresponding execution of <a class="citerefentry" href="glEnd.xml"><span class="citerefentry"><span class="refentrytitle">glEnd</span></span></a>. |
| 721 | </p><p> |
| 722 | <code class="constant">GL_INVALID_OPERATION</code> is generated if <code class="function">glMap2</code> is called and the value |
| 723 | of <code class="constant">GL_ACTIVE_TEXTURE</code> is not <code class="constant">GL_TEXTURE0</code>. |
| 724 | </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="associatedgets"></a><h2>Associated Gets</h2><p> |
| 725 | <a class="citerefentry" href="glGetMap.xml"><span class="citerefentry"><span class="refentrytitle">glGetMap</span></span></a> |
| 726 | </p><p> |
| 727 | <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MAX_EVAL_ORDER</code> |
| 728 | </p><p> |
| 729 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_VERTEX_3</code> |
| 730 | </p><p> |
| 731 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_VERTEX_4</code> |
| 732 | </p><p> |
| 733 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_INDEX</code> |
| 734 | </p><p> |
| 735 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_COLOR_4</code> |
| 736 | </p><p> |
| 737 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_NORMAL</code> |
| 738 | </p><p> |
| 739 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_TEXTURE_COORD_1</code> |
| 740 | </p><p> |
| 741 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_TEXTURE_COORD_2</code> |
| 742 | </p><p> |
| 743 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_TEXTURE_COORD_3</code> |
| 744 | </p><p> |
| 745 | <a class="citerefentry" href="glIsEnabled.xml"><span class="citerefentry"><span class="refentrytitle">glIsEnabled</span></span></a> with argument <code class="constant">GL_MAP2_TEXTURE_COORD_4</code> |
| 746 | </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="seealso"></a><h2>See Also</h2><p> |
| 747 | <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a>, |
| 748 | <a class="citerefentry" href="glColor.xml"><span class="citerefentry"><span class="refentrytitle">glColor</span></span></a>, |
| 749 | <a class="citerefentry" href="glEnable.xml"><span class="citerefentry"><span class="refentrytitle">glEnable</span></span></a>, |
| 750 | <a class="citerefentry" href="glEvalCoord.xml"><span class="citerefentry"><span class="refentrytitle">glEvalCoord</span></span></a>, |
| 751 | <a class="citerefentry" href="glEvalMesh.xml"><span class="citerefentry"><span class="refentrytitle">glEvalMesh</span></span></a>, |
| 752 | <a class="citerefentry" href="glEvalPoint.xml"><span class="citerefentry"><span class="refentrytitle">glEvalPoint</span></span></a>, |
| 753 | <a class="citerefentry" href="glMap1.xml"><span class="citerefentry"><span class="refentrytitle">glMap1</span></span></a>, |
| 754 | <a class="citerefentry" href="glMapGrid.xml"><span class="citerefentry"><span class="refentrytitle">glMapGrid</span></span></a>, |
| 755 | <a class="citerefentry" href="glNormal.xml"><span class="citerefentry"><span class="refentrytitle">glNormal</span></span></a>, |
| 756 | <a class="citerefentry" href="glTexCoord.xml"><span class="citerefentry"><span class="refentrytitle">glTexCoord</span></span></a>, |
| 757 | <a class="citerefentry" href="glVertex.xml"><span class="citerefentry"><span class="refentrytitle">glVertex</span></span></a> |
| 758 | </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="Copyright"></a><h2>Copyright</h2><p> |
| 759 | Copyright <span class="trademark"></span>© 1991-2006 |
| 760 | Silicon Graphics, Inc. This document is licensed under the SGI |
| 761 | Free Software B License. For details, see |
| 762 | <a class="ulink" href="http://oss.sgi.com/projects/FreeB/" target="_top">http://oss.sgi.com/projects/FreeB/</a>. |
| 763 | </p></div></div></body></html> |